Machine learning with sub-diffraction resolution in the photon-counting regime
arXiv:2406.03179 · doi:10.1007/s42484-025-00262-8
Abstract
The resolution of optical imaging is classically limited by the width of the point-spread function, which in turn is determined by the Rayleigh length. Recently, spatial-mode demultiplexing (SPADE) has been proposed as a method to achieve sub-Rayleigh estimation and discrimination of natural, incoherent sources. Here we show that SPADE yields sub-diffraction resolution in the broader context of image classification. To achieve this goal, we outline a hybrid machine learning algorithm for image classification that includes a physical part and a computational part. The physical part implements a physical pre-processing of the optical field that cannot be simulated without essentially reducing the signal-to-noise ratio. In detail, a spatial-mode demultiplexer is used to sort the transverse field, followed by mode-wise photon detection. In the computational part, the collected data are fed into an artificial neural network for training and classification. As a case study, we classify images from the MNIST dataset after severe blurring due to diffraction. Our numerical experiments demonstrate the ability to classify highly blurred images that would be otherwise indistinguishable by direct imaging without the physical pre-processing of the optical field.
v2: title changed + extended results. Accepted version
References in corpus (24)
- Longer-Baseline Telescopes Using Quantum Repeaters
- Far-field Superresolution of Thermal Electromagnetic Sources at the Quantum Limit
- Beating Rayleigh's Curse by Imaging Using Phase Information
- Multiparameter Quantum Metrology of Incoherent Point Sources: Towards Realistic Superresolution
- Ultimate precision bound of quantum and sub-wavelength imaging
- Optical Interferometry with Quantum Networks
- A modern description of Rayleigh's criterion
- Quantum-limited estimation of the axial separation of two incoherent point sources
- The quantum limit to incoherent imaging is achieved by linear interferometry
- Quantum limited superresolution of an incoherent source pair in three dimensions
- Quantum-optimal detection of one-versus-two incoherent optical sources with arbitrary separation
- Quantum-optimal detection of one-versus-two incoherent sources with arbitrary separation
- Superresolution Limits from Measurement Crosstalk
- Quantum hypothesis testing for exoplanet detection
- Resolution limits of spatial mode demultiplexing with noisy detection
- Quantum limits of superresolution in a noisy environment
- Subwavelength quantum imaging with noisy detectors
- Identifying Objects at the Quantum Limit for Super-Resolution Imaging
- Ultra-sensitive separation estimation of optical sources
- Passive superresolution imaging of incoherent objects
- Single-photon sub-Rayleigh precision measurements of a pair of incoherent sources of unequal intensity
- Imaging stars with quantum error correction
- Spatial-mode-demultiplexing for enhanced intensity and distance measurement
- Ultimate limits of exoplanet spectroscopy: a quantum approach